Much was made of the matchup, as it was the first between the two teams since Steve Yzerman left the Red Wings organization to become general manager of the Lightning.
Datsyuk made it 2-0 with 5:03 left in the period, pouncing on a rebound and swatting it past a sprawling Roloson on the backhand.
The Lighting would briefly rally in the second period, scoring twice in 2:47 to tie the game.
With 8:09 left in the period, Victor Hedman wristed a shot from just inside the blue line that deflected past Detroit goalie Jimmy Howard to get Tampa Bay on the board.
With 5:22 left, Steve Downie snapped a loose puck past Howard to make it 2-2.
The Red Wings regained control 1:56 later, when a Niklas Kronwall shot deflected off of Cleary's skate and into the net for a power play goal.
Justin Abdelkader put a rebound chance past Roloson from the edge of the crease with 2:00 remaining to restore the two-goal lead.
Datsyuk's second of the night came with 8:21 left in the third period. He was left uncovered to race into the Tampa zone and take a feed from Jiri Hudler before snapping a shot past Roloson.
Darren Helm wrapped up the game's scoring with 1:51 left in the game, turning a turnover at the Lightning blue line into a breakaway goal.
Detroit's power play goals gave them two on three tries with the extra attacker. Tampa Bay went scoreless on five chances with the man-advantage.
Howard stopped 38 of the 40 shots he faced on the night. Roloson made 25 saves on 31 shots.
The Red Wings continue their Florida road trip on Friday night as they visit the Panthers.
Notes: Brad Stuart returned to the Detroit lineup after missing 15 games with a broken jaw... Ruslan Salei was given the night off to spend more time with his California-based family. He will return to the lineup against the Panthers.
Credit: Clark Rasmussen